L <sup> q </sup>-spectra of self-affine measures: closed forms, counterexamples, and split binomial sums
نویسندگان
چکیده
Abstract We study L q -spectra of planar self-affine measures generated by diagonal matrices. introduce a new technique for constructing and understanding examples based on combinatorial estimates the exponential growth certain split binomial sums. Using this approach we disprove theorem Falconer Miao from 2007 conjecture 2008 concerning closed form expression generalised dimensions generic measures. also answer question Fraser 2016 in negative proving that natural does not generally give -spectrum. As further application provide whose exhibit types phase transitions. Finally, non-trivial bounds -spectra, which cases yield sharp results.
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2021
ISSN: ['0951-7715', '1361-6544']
DOI: https://doi.org/10.1088/1361-6544/ac14a2